Coefficient conditions for harmonic close-to-convex functions

TL;DR

This paper establishes new coefficient-based conditions that ensure harmonic functions in the unit disk are close-to-convex, providing illustrative examples and domain images to demonstrate these criteria.

Contribution

It introduces novel coefficient conditions for harmonic close-to-convex functions, expanding the understanding of their geometric properties.

Findings

Derived sufficient coefficient conditions for harmonic close-to-convexity.

Provided examples illustrating the application of these conditions.

Enumerated image domains of functions satisfying the new criteria.

Abstract

New sufficient conditions, concerned with the coefficients of harmonic functions $f(z)=h(z)+\bar{g(z)}$ in the open unit disk $\mathbb{U}$ normalized by $f(0)=h(0)=h'(0)-1=0$, for $f(z)$ to be harmonic close-to-convex functions are discussed. Furthermore, several illustrative examples and the image domains of harmonic close-to-convex functions satisfying the obtained conditions are enumerated.